Freewheel replacement for a touring tandem bike

I have an older touring tandem bike that we use to go on long trips. The gear setup is 3×7. I noticed that we hardly ever use the smallest 3 cogs on the freewheel (of course together with the largest chainwheel). We also struggle on the climbs, so I would like to change the freewheel to help us on the climbs.

The freewheel setup is 13-30. I am thinking or replacing it with something like 16-36 or similar. The problem is that I haven’t found a 7-gear freewheel with such a setup. The only freewheel with a better setup that I’ve found is the Sunrace MFM300 7DV. But the difference seems to be major only on the largest cog (30 vs 34).

This is the current freewheel:

Do you know where I could buy a freewheel with a better setup for climbing than this?

Or would you recommend that I do one of the following?

1. Change the chainrings – from what I see, I would have to
   change all 3 of them, as the screws on the smallest chainring would
   not allow changing it with a smaller one. Seems to involved for my
   bike repairing skills.
2. Change the back wheel entirely to support a newer, cassette style type of cogs. One problem is that
   the back wheel is also fitted with a drum brake on the left side, no idea how to
   properly re-fit it on a new wheel. Also, I would like to keep as many original parts as posible on the bike.
3. Changing the wheel’s hub to a freehub to support a casette. This has the
   advantage that the bike will stay with most of its original parts,
   but would be really involved. Again, might be difficult to impossible to re-fit the drum brake.

Advices welcome, I’m not an expert bike tehnician.

Chainring sizes: 54-48-40.

Current chainrings:

Chainrings’ Bolt: